轉子撓扭耦合共振之非線性分析

Nonlinear Analysis of a Rotor due to Coupled Lateral-Torsional Vibration

康淵(Y. Kang) ； 簡守謙(S.-C. Jen) ； 賴志錫(Z.-S. Lai)

《中原學報》 24卷1期 (1996/01) Pp. 47-60

https://doi.org/10.6358/JCYU.199601.0047

摘要

轉動機械在撓－扭耦合共振之轉速範圍內，其運動之行為極為複雜且不規則，此種運動模式，比起其他速度範圍，顯得激烈而混亂，往往會造成機構之疲勞，而引致損壞。根據系統之非線性動態分析，可以模擬出混沌現象的發生或分歧（Bifurcation）轉變過程，其運動之行為將趨於混亂並可能喪失週期性。本文將針對兩種撓－扭耦合之轉子來探討耦合振動對系統非線性動態行為所造成之影響及其運動模式，作為旋轉機械設計上考慮之因素。而對於非線性方程式之分析方法，在此採用四階之Runge-Kutta法作為數值之積分，解得系統橫向振動與扭轉振動在彼此耦合之條件下之動態行為，並利用相平面，對時問之位移軌跡，以及Poincare’切平面等之定性方法來求系統於某些條件下之運動行為，並利用分歧圖來觀測系統之整體動態行為變化。

關鍵字

轉子 ； 撓一扭耦合共振 ； 混沌振盪 ； 分歧

並列摘要

Transverse vibrations of a rotor-bearing system are coupled with
torsional oscilations through mass essentricity. The effect in coupled torsional-transverse vibration is that combination-resonances may be induced and the rotor has destructively large amplitudes.
In this study, two rotor systems with coupled torsional transverse vibrations are considered. The first model of an unbalanced rotor, driven by torsion-flexible shaft through a coupling is used to investigate the effect of load torque applied on overhung disk.
The second model of an unbalanced rotor mounted between two bearings. The nonlinear equations of motions of these rotor systems are solved numerically by using Runge-Kutta method.
The results of time history, frequency spectra, phase plane, Poincare’ map, and bifurcation diagram have been obtained. The quasi periodic responses and chaotic motions can be observed within combination resonances.

並列關鍵字

rotor ； coupled lateral-torsional resonance ； chaotic oscillation ； bifurcation